On q-functional equations and excursion moments

Richard C (2009)

Publication Type: Journal article

Publication year: 2009


Publisher: Elsevier

Book Volume: 309

Pages Range: 207--230

Journal Issue: 1

DOI: 10.1016/j.disc.2007.12.072


We analyse q-functional equations arising from tree-like combinatorial structures, which are counted by size, internal path length, and certain generalisations thereof. The corresponding counting parameters are labelled by a positive integer k. We show the existence of a joint limit distribution for these parameters in the limit of infinite size, if the size generating function has a square root as dominant singularity. The limit distribution coincides with that of integrals of kth powers of the standard Brownian excursion. Our approach yields a recursion for the moments of the limit distribution. It can be used to analyse asymptotic expansions of the moments, and it admits an extension to other types of singularity.

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Richard, C. (2009). On q-functional equations and excursion moments. Discrete Mathematics, 309(1), 207--230. https://dx.doi.org/10.1016/j.disc.2007.12.072


Richard, Christoph. "On q-functional equations and excursion moments." Discrete Mathematics 309.1 (2009): 207--230.

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